DB Or Not DB? Everything You Ever Wanted To Know About .
dB or not dB?Everything you everwanted to knowabout decibels butwere afraid to ask . . .True or false: 30 dBm 30 dBm 60 dBm?Why does 1% work out to be -40 dB one time but then 0.1 dB or 0.05 dB thenext time? These questions sometimes leave even experienced engineersscratching their heads. Decibels are found everywhere, including powerlevels, voltages, reflection coefficients, noise figures, field strengths andmore. What is a decibel and how should we use it in our calculations? ThisApplication Note is intended as a refresher on the subject of decibels.A. Winter, 05.2014Application1MA98ApplicationNoteNote1MA98 8eProducts: Signal generators, spectrum analyzers, test receivers, networkanalyzers, power meters, audio analyzers
8 8e1MA98 8e1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332Whyuse decibelsin our calculations?Why use decibelsin our calculations?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333DefinitionofdB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Definition of dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 What does dBm mean? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4What doesdBm mean? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 What’s the difference between voltage decibels and power decibels? . . . 5What’s6 thedifferencebetweenvoltage decibels and power decibels?. . . . . 65Whatis a level?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .What isalevel?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867 Attenuation and gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .connectionAttenuation Seriesand gain. . . . . . . .of . .two-port. . . . . .circuits:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 988ConversionfromdecibelstopercentageandSeries connection of two-port circuits:. . . . . . . . vice. . . .versa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Converting%voltagetodecibelsandviceversa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Conversion from decibels to percentage and vice versa . . . . . . . . . . . . . . . 99Converting % power to decibels and vice versa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Converting % voltage to decibels to percentage and vice versa. . . . . . . 9Converting % voltage more or less to decibels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Converting% powerdecibelsandvice versa. . . . . . . 1110Converting% topowermore toor percentageless to decibels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Converting% voltageor less todecibels. . . . . . . . . . . . . . . . . . . 12119 Using dBvalues inmorecomputations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Converting% powerless to decibels. . . . . . . . . . . . . . . . . . . . 1211Addingpowermorelevelsor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Measuringsignals at theUsing dB valuesin computations. . noise. . . . .limit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1212AddinglevelsvoltagesAdding power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1312Peakvoltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Measuring signals at the noise limit. . . . . . . . . . . . . . . . . . . . . . . . . . . . 161210 What do we measure in decibels? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Adding voltages.13Signal-to-noise ratio (S/N) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Peak voltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1816Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .What do weAveragingmeasure noisein decibels?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1917signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Noise factor,Signal-to-noiserationnoise(S/N)figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2017Phasenoise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20Noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18S parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Averagingnoise signals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2219VSWR and reflection coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Noise factor,noisefigure.20Field strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Phase noise. .20Antenna gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25S parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2522Crest. .factorChannelpowercoefficientand adjacentVSWR andreflection. . . channel. . . . . . .power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2723ModulationField strength. . . . . .quality. . . . .EVM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2824DynamicrangeofA/DandD/Aconverters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29Antenna gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25dB (FS) (Full Scale) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Crest factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Sound pressure level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Channel Weightedpower andadjacentchannelpower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3127soundpressurelevel dB(A)Modulationquality ofworthEVMknowing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322811 A few numbersDynamicTablerangeforofconversionA/D and D/Aconverters. . .and. . .linear. . . . values . . . . . . . . . . . . . . . . . . . . . . . . . . . 3229betweendecibelsTableScale)for addingdB (FS) (Full. . . . .decibel. . . . . values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3330Some moreusefulSound pressurelevel. . . . . values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3430Otherreferencequantities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34Weighted sound pressure level dB(A). . . . . . . . . . . . . . . . . . . . . . . . . . 31Accuracy, number of decimal places . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35A few 12numbersworthappknowing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3532SmartphonedB arvalues.3213 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Tablefor addinginformationdecibel values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353314 Additional. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Some more useful values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Other reference quantities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Accuracy, number of decimal places. . . . . . . . . . . . . . . . . . . . . . . . . . . 35Smartphone app dB Calculator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Additional information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3522Rohde& SchwarzRohde& Schwarz
Introduction1 IntroductionIntroduction%, dB, dBm and dB(µV/m) are important concepts that every engineershould understand in his (or her) sleep. Because if he doesn’t, he is boundto be at a disadvantage in his work . When these terms come up indiscussions with customers or colleagues, he will have trouble focusing onthe real issue if he is busy wondering whether 3 dB means a factor of 2 or 4(or something else) . It is well worth the effort to review these concepts fromtime to time and keep familiar with them .While this Application Note is not intended as a textbook, it will help torefresh your knowledge of this topic if you studied it before or provide adecent introduction if it is new to you .When it comes to writing formulas and units, we have followed theinternational standards as originally specified in ISO 31 and IEC 27,currently known as ISO / IEC 80000 (or else we have indicated whereit is common practice to deviate from the standard).2 WhyWhy lations?Engineers have to deal with numbers on an everyday basis, and some ofthese numbers can be very large or very small . In most cases, what ismost important is the ratio of two quantities . For example, a mobile radiobase station might transmit approx . 80 W of power (antenna gain included) .The mobile phone receives only about 0 .000 000 002 W, which is0 .000 000 002 5 % of the transmitted power .Whenever we must deal with large numerical ranges, it is convenient to usethe logarithm of the numbers . For example, the base station in our exampletransmits at 49 dBm while the mobile phone receives -57 dBm, producinga level difference of 49 dBm - (-57 dBm) 106 dB .Another example: If we cascade two amplifiers with power gains of 12 and16, respectively, we obtain a total gain of 12 times 16 192 (which you canhopefully calculate in your head – do you?) . In logarithmic terms, the twoamplifiers have gains of 10 .8 dB and 12 dB, respectively, producing a totalgain of 22 .8 dB, which is definitely easier to calculate .When expressed in decibels, we can see that the values are a lot easier tomanipulate . It is a lot easier to add and subtract decibel values in your headthan it is to multiply or divide linear values . This is the main reason we liketo make our computations in decibels .3 DefinitionDefinitionofofdBdBAlthough the base 10 logarithm of the ratio of two power values is adimensionless quantity, it has units of “Bel” in honor of the inventor of thetelephone (Alexander Graham Bell) . In order to obtain more manageablenumbers, we use the dB (decibel, where “deci” stands for one tenth)instead of the Bel for computation purposes . We have to multiply the Belvalues by 10 (just as we need to multiply a distance by 1000 if we want touse millimeters instead of meters) . P a 10 log10 1 dB P2 1MA98 8e1MA98 8e33Rohde& SchwarzRohde& Schwarz
What does dBm mean?As mentioned above, the advantage of using decibels is that the hugerange of the signals commonly encountered in telecommunications andradio frequency engineering can be represented with more manageablenumbers .Example:P1 is equal to 200 W and P2 is equal to 100 mW. What is theirratio a in dB? Pa 10 log 10 1 P2 dB 10 log 10 2000 dB 33.01 dB Of course, before dividing these power levels, we have to convert them tothe same unit, i.e. W or mW. We won’t obtain the correct result if we justdivide 200 by 100 .Nowadays, we use base 10 logarithms almost exclusively . The abbreviationfor a base 10 logarithm is lg . In older textbooks, you will sometimes see thenatural logarithm used, which is the base e logarithm (e approx . 2 .718) . Inthis Application Note, we use only the base 10 logarithm which weabbreviate with lg without indicating the base furtheron .Of course, it is also possible to convert decibels back to linear values . Wemust first convert from dB to Bel by dividing the value by 10 . Then, we mustraise the number 10 (sincewe are using a base 10a / dBP1logarithm) to this power:10P2 10Example:a 33.01 dB, what is P1 / P2?After first computing 33.01 / 10 3.301, we obtain:P1 103.301 1999.9P244 WhatdoesdBmdBmmean?mean?What doesIf we refer an arbitrary power value to a fixed reference quantity, thelogarithmic ratio of the two values yields a new absolute quantity . Thisquantity is defined as a level .The reference quantity most commonly used in telecommunications andradio frequency engineering is a power of 1 mW (one thousandth of oneWatt) into 50 Ohm .The general power ratio P1 to P2 now becomes a ratio of P1 to 1 mW . Thelogarithmic ratio provides the level L . According to IEC 27 the referencevalue had to be indicated in the level index: P LP (re 1 mW) 10 lg 1 dB 1 mW or the short form: P LP / 1 mW 10 lg 1 dB 1 mW For example 5 mW correspondent to a level of LP/1mW 6 .99 dB .1MA98 8e1MA98 8e44Rohde& SchwarzRohde& Schwarz
What’s the difference between voltage decibels andpower decibels?To denote the reference of 1 mW, the ITU introduced the unit dBm . Thisunit is more common than the IEC 27 terminology, and will be usedthroughout this paper .To give you a feeling for the orders of magnitude which tend to occur, hereare some examples: The output power range of signal generators extendstypically from -140 dBm to 20 dBm or 0 .01 fW (femto Watt) to 0 .1 W .Mobile radio base stations transmit at 43 dBm or 20 W . Mobile phonestransmit at 10 dBm to 33 dBm or 10 mW to 2 W . Broadcast transmittersoperate at 70 dBm to 90 dBm or 10 kW to 1 MW .55 What’sthe hat’s thevoltagedecibelsand powerdecibels?andpower decibels?First of all, please forget everything you’ve ever heard about voltage andpower decibels . There is only one type of decibel, and it represents a ratioof two power levels P1 and P2 . Of course, any power level can be expressedas a voltage if we know the resistance .P1 22U1Uand P2 2R1R2We can compute the logarithmic ratio as follows: U12 R2 P1 a 10 lg dB 10 lg 2 dB P2 U 2 R1 Using the following 3 familiar identities, 1 log log x x log x y y log x log xy log x log y we obtain (again using lg to mean the base 10 logarithm): U 2 R R P U a 10 lg 1 dB 10 lg 1 2 2 dB 20 lg 1 dB 10 lg 1 dB R2 P2 U2 U 2 R1 Note the minus sign in front of the resistance term .In most cases, the reference resistance is equal for both power levels, i .e .R1 R2 . Since10 lg 1 0we can simplify as follows: P U a 10 lg 1 dB 20 lg 1 dB P2 U2 1MA98 8e1MA98 8e55(simplified for R1 R2!)Rohde& SchwarzRohde& Schwarz
What is a level?This also explains why we use 10·lg for power ratios and 20·lg for voltageratios .Caution:(Very important!) This formula is valid only if R1 R2. If, assometimes occurs in television engineering, we need to takeinto account a conversion from 75 Ohm to 50 Ohm, we need toconsider the ratio of the resistances.Conversion back to linear values is the same as before . For voltage ratios,2we must divide the value a by 20 since we use U and decibels (20 2·10,22 fr
Everything you ever wanted to know about decibels but were afraid to ask . . . Application Note 1MA98 A. Winter, 05.2014 True or false: 30 dBm 30 dBm 60 dBm? Why does 1% work out to be -40 dB one time but then 0.1 dB or 0.05 dB the next time? These questions sometimes
Everything's alright, yes. Everything's alright, yes. MARY MAGDALENE Sleep and I shall soothe you, calm you and anoint you – Myrrh for your hot forehead. Oh, then you'll feel Everything's alright, yes, everything's fine, And it's cool and the ointment's sweet For the fire in your head and feet. Close your eyes, close your eyes, And relax.
Feb. 20, 2006 MSR-TR-2006-23 Microsoft Bay Area Research Center San Francisco, CA, 94105 1 02/21/2006 . MyLifeBits: A Personal Database for Everything . photos, and video as well as everything born digital e.g. office documents, email, digital photos. It evolved to have a goal of storing everything that could be captured. The later included
Twilight—never-been-a-pony Twilight—what you need to know is that Princess Twilight Sparkle knows everything about friendship.” “Everything?” asked Twilight Sparkle, amazed. “Everything,” agreed all the Equestria Girls together. “That’s not true!” protested Princess Twilight. “Every
Everything’s An Argument: Argumentation Vocabulary Guide Welcome to English 110! As a student, you may be familiar with some of the terms used in your textbook Everything’s An Argument. This resource has been created to help you navigate through unfamiliar terms in your textbook and to show how they can be used in your future writing.
baker, or a candlestick maker. Everything, everything you do must reflect upon you and the level of integrity in which you provide that service or product to your customer. Your business operations manual must think of everything. And then deliver consistently, every time.
Everything You Ever Really Needed to Know About Personal Finance On Just One Page . The cover of this document tells you the whole story. Everything you really need to know abut personal finance can be summarized in just one page. Spend less than you earn. Earn more. Live frugal. Do something sensible with the difference. Control your
Jun 28, 2018 · 245(I): EVERYTHING YOU ALWAYS WANTED TO KNOW BUT WERE AFRAID TO ASK . 4 . 245(I): EVERYTHING YOU ALWAYS WANTED TO KNOW BUT WERE AFRAID TO ASK JUNE 2018 . timeframe, on or before April 30, 2001, there is no visa preference category for siblings of permanent residents. Even though Luis late
Everything You Ever Wanted to Know About Laminates but Were Afraid to Ask Introduction to the 9th Edition Dear Reader, It has been over 25 years since the earliest edition of “Everything You Ever Wanted to Know About Laminates but Were Afraid to
